This is a nice article outlining what is commonly referred to as the illuminati. Who they are, what they do, how they got started, where they came from.
This is a good article to use as a starting point to introduce someone else to the concept.
What you could call “modern Illuminati” has originated from the original bavarian Illuminati created by Adam Weishaupt.
“The great strength of our Order lies in its concealment; let it never appear in any place in its own name, but always covered by another name, and another occupation – Adam Weishaupt.”
There is reasonable evidence that groups like Skull & Bones, Bohemian Grove, Freemansonry (only top degree members) and other secret societies are or being controlled by the “modern Illuminati”.